/// <summary>
/// Initializes a new <see cref="ConnectedSubgraph"/> instance with the specified main
/// vertex.
/// </summary>
/// <param name="mainVertex">The main vertex of the connected subgraph.</param>
/// <remarks>
/// <para>The main vertex of a connected subgraph is used to identify all other vertices in
/// it and is the only vertex that is certain to remain in the connected subgraph when
/// edges are removed.</para>
/// </remarks>
public ConnectedSubgraph(Vertex mainVertex)
{
_mainVertex = mainVertex;
_connectedVertices = new HashSet<Vertex> { _mainVertex };
_weaklyConnectedSubgraphs = new Dictionary<Vertex, WeaklyConnectedSubgraph>
{
// The main vertex of the connected subgraph belongs to its strongly connected
// portion by definition
{ _mainVertex, null },
};
AddOtherConnectedVertices(_mainVertex);
}
/// <summary>
/// Adds a vertex to the list of vertices in the weakly connected portion of the connected
/// subgraph.
/// </summary>
/// <param name="vertex">The vertex which should be added to the list of vertices.</param>
public void AddConnectedVertex(Vertex vertex)
{
_connectedVertices.Add(vertex);
}
/// <summary>
/// Initializes a new <see cref="WeaklyConnectedSubgraph"/> instance with the specified
/// anshor vertex.
/// </summary>
/// <param name="anchorVertex">The anchor vertex of the weakly connected portion of the
/// connected subgraph.</param>
/// <remarks>
/// <para>The anchor vertex is the only vertex from the strongly connected portion of the
/// connected subgraph which connects it to the weakly connected portion.</para>
/// </remarks>
public WeaklyConnectedSubgraph(Vertex anchorVertex)
{
_anchorVertex = anchorVertex;
_connectedVertices = new HashSet<Vertex>();
}
/// <summary>
/// Checks if a vertex belongs to the weakly connected portion of the connected subgraph.
/// </summary>
/// <param name="vertex">The vertex which should be checked.</param>
/// <returns><see langword="true"/> if the vertex belongs to the weakly connected portion
/// of the connected subgraph.
/// </returns>
public bool ContainsVertex(Vertex vertex)
{
return _connectedVertices.Contains(vertex);
}
/// <summary>
/// Adjusts the weakly connected portions of the connected subgraph which two vertices
/// might belong to immediately after adding an edge between them, possibly reintegrating
/// them back into the strongly connected portion of the connected subgraph.
/// </summary>
/// <param name="vertex1">The first vertex which might belong to a weakly connected portion
/// of the connected subgraph.</param>
/// <param name="vertex2">The second vertex which might belong to a weakly connected
/// portion of the connected subgraph.</param>
private void AdjustWeaklyConnectedSubgraphs(Vertex vertex1, Vertex vertex2)
{
WeaklyConnectedSubgraph weaklyConnectedSubgraph1 = _weaklyConnectedSubgraphs[vertex1];
WeaklyConnectedSubgraph weaklyConnectedSubgraph2 = _weaklyConnectedSubgraphs[vertex2];
// If both vertices belong to the same weakly connected portion of the connected
// subgraph or to the strongly connected portion of the connected subgraph nothing
// needs to be recalculated
if (weaklyConnectedSubgraph1 == weaklyConnectedSubgraph2)
return;
if (weaklyConnectedSubgraph1 == null)
{
// If the first vertex belongs to the strongly connected portion of the connected
// subgraph and the second vertex belongs to a weakly connected portion, only
// integrate the weakly connected portion back into the strongly connected portion
// if the first vertex is the main vertex of the connected subgraph or differs from
// the anchor vertex of the weakly connected portion
if (vertex1 == _mainVertex || vertex1 != weaklyConnectedSubgraph2.AnchorVertex)
IntegrateWeaklyConnectedSubgraph(weaklyConnectedSubgraph2);
}
else if (weaklyConnectedSubgraph2 == null)
{
// If the second vertex belongs to the strongly connected portion of the connected
// subgraph and the first vertex belongs to a weakly connected portion, only
// integrate the weakly connected portion back into the strongly connected portion
// if the second vertex is the main vertex of the connected subgraph or differs
// from the anchor vertex of the weakly connected portion
if (vertex2 == _mainVertex || vertex1 != weaklyConnectedSubgraph1.AnchorVertex)
IntegrateWeaklyConnectedSubgraph(weaklyConnectedSubgraph1);
}
else
{
// If both vertices belong to different weakly connected portions of the connected
// subgraph, integrate both of them back into the strongly connected portion
IntegrateWeaklyConnectedSubgraph(weaklyConnectedSubgraph1);
IntegrateWeaklyConnectedSubgraph(weaklyConnectedSubgraph2);
}
}
/// <summary>
/// Adds a vertex to the list of vertices in the connected subgraph and then recursively
/// adds all vertices directly connected to it. The vertex is added to the list because it
/// is directly connected to a base vertex which is already in the list of vertices.
/// </summary>
/// <param name="vertex">The vertex which should be added to the list of vertices.</param>
/// <param name="baseVertex">The base vertex which the specified vertex is directly
/// connected to.</param>
/// <remarks>
/// <para>If the specified vertex is not yet in the list of vertices, it is be added to a
/// suitable weakly connected portion of the connected subgraph.</para>
/// <para>If the specified vertex is already in the list of vertices, the method checks if
/// they belong to one or two weakly connected portions of the connected subgraph and
/// integrates them back into the strongly connected portion of the connected subgraph, if
/// eligible.</para>
/// </remarks>
private void AddConnectedVertex(Vertex vertex, Vertex baseVertex)
{
if (_connectedVertices.Contains(vertex))
{
if (!IsVertexStronglyConnected(vertex))
AdjustWeaklyConnectedSubgraphs(vertex, baseVertex);
else if (!IsVertexStronglyConnected(baseVertex))
AdjustWeaklyConnectedSubgraphs(baseVertex, vertex);
}
else
{
_connectedVertices.Add(vertex);
WeaklyConnectedSubgraph weaklyConnectedSubgraph =
(IsVertexStronglyConnected(baseVertex)
? new WeaklyConnectedSubgraph(baseVertex)
: _weaklyConnectedSubgraphs[baseVertex]);
weaklyConnectedSubgraph.AddConnectedVertex(vertex);
_weaklyConnectedSubgraphs.Add(vertex, weaklyConnectedSubgraph);
AddOtherConnectedVertices(vertex);
}
}
/// <summary>
/// Adds all vertices which are directly connected to a specific base vertex to the list of
/// vertices in the connected subgraph. The base vertex itself must have already been added
/// to the list of vertices in the connected subgraph.
/// </summary>
/// <param name="baseVertex">The base vertex which is already in the list of vertices.
/// </param>
private void AddOtherConnectedVertices(Vertex baseVertex)
{
foreach (Vertex directlyConnectedVertex in baseVertex.ConnectedVertices)
{
AddConnectedVertex(directlyConnectedVertex, baseVertex);
}
}
/// <summary>
/// Checks if a vertex belongs to the strongly connected portion of the connected subgraph.
/// </summary>
/// <param name="vertex">The vertex which should be checked.</param>
/// <returns><see langword="true"/> if the vertex belongs to the strongly connected portion
/// of the connected subgraph.</returns>
public bool IsVertexStronglyConnected(Vertex vertex)
{
return (_weaklyConnectedSubgraphs[vertex] == null);
}
/// <summary>
/// Checks if adding an edge between two vertices in the connected subgraph will expand
/// the strongly connected portion of the connected subgraph.
/// </summary>
/// <param name="vertex1">The first vertex which might be connected.</param>
/// <param name="vertex2">The second vertex which might be connected.</param>
/// <returns>see langword="true"/> if adding an edge between the two vertices will expand
/// the strongly connected portion of the connected subgraph.</returns>
public bool CheckWillConnectStrongly(Vertex vertex1, Vertex vertex2)
{
WeaklyConnectedSubgraph weaklyConnectedSubgraph1 = _weaklyConnectedSubgraphs[vertex1];
WeaklyConnectedSubgraph weaklyConnectedSubgraph2 = _weaklyConnectedSubgraphs[vertex2];
// If both vertices belong to the same weakly connected portion of the connected
// subgraph or to the strongly connected portion of the connected subgraph, adding the
// edge will not expand the strongly connected portion
if (weaklyConnectedSubgraph1 == weaklyConnectedSubgraph2)
return false;
// If the first vertex belongs to the strongly connected portion of the connected
// subgraph, adding the edge will expand the strongly connected portion when the first
// vertex is the main vertex of the connected subgraph or differs from the anchor
// vertex of the weakly connected portion of the connected subgraph which contains the
// second vertex
if (weaklyConnectedSubgraph1 == null)
{
return (vertex1 == _mainVertex
|| vertex1 != weaklyConnectedSubgraph2.AnchorVertex);
}
// If the second vertex belongs to the strongly connected portion of the connected
// subgraph, adding the edge will expand the strongly connected portion when the second
// vertex is the main vertex of the connected subgraph or differs from the anchor
// vertex of the weakly connected portion of the connected subgraph which contains the
// first vertex
if (weaklyConnectedSubgraph2 == null)
{
return (vertex2 == _mainVertex
|| vertex1 != weaklyConnectedSubgraph1.AnchorVertex);
}
// If both vertices belong to different weakly connected portions of the connected
// subgraph, adding the edge will integrate both weakly connected portions back into
// the strongly connected portion
return true;
}
/// <summary>
/// Checks if the vertex is directly connected to another vertex.
/// </summary>
/// <param name="otherVertex">The other vertex which should be checked.</param>
/// <returns><see langword="true"/> if the specified vertex is directly connected to the
/// current one.</returns>
public bool IsConnectedToVertex(Vertex otherVertex)
{
return _connectedVertices.Contains(otherVertex);
}
/// <summary>
/// Removes the edge between the vertex and another vertex.
/// </summary>
/// <param name="otherVertex">The vertex which should be disconnected from the current one.
/// </param>
/// <exception cref="InvalidOperationException">
/// An attempt is made to disconnect the vertex from itself.
///
/// -or-
/// No edge between the two vertices exists.
/// </exception>
/// <remarks>
/// <para>The method removes the specified vertex from the list of directly connected
/// vertices of the current vertex and vice versa.</para>
/// </remarks>
public void DisconnectFromVertex(Vertex otherVertex)
{
if (this == otherVertex)
throw new InvalidOperationException("A vertex cannot be connected to itself.");
if (!IsConnectedToVertex(otherVertex))
throw new InvalidOperationException("No edge between the two vertices exists.");
_connectedVertices.Remove(otherVertex);
otherVertex._connectedVertices.Remove(this);
}
/// <summary>
/// Adds an edge between the vertex and another vertex.
/// </summary>
/// <param name="otherVertex">The vertex which should be connected to the current one.
/// </param>
/// <exception cref="InvalidOperationException">
/// An attempt is made to connect the vertex to itself.
///
/// -or-
/// An edge between the two vertices already exists.
/// </exception>
/// <remarks>
/// <para>The method adds the specified vertex to the list of directly connected vertices
/// of the current vertex and vice versa.</para>
/// </remarks>
public void ConnectToVertex(Vertex otherVertex)
{
if (this == otherVertex)
throw new InvalidOperationException("A vertex cannot be connected to itself.");
if (IsConnectedToVertex(otherVertex))
{
throw new InvalidOperationException(
"An edge between the two vertices already exists.");
}
_connectedVertices.Add(otherVertex);
otherVertex._connectedVertices.Add(this);
}